Non-profit sector and regional well-being in Italy

ABSTRACT This paper investigates the link between the non-profit sector and regional well-being, conceiving and measuring the latter following a multidimensional approach that considers several factors affecting the quality of life of populations. A cross-sectional econometric analysis conducted on a sample of 106 Italian provinces shows findings robust to several specifications and scenarios consistent with our hypothesis that the non-profit sector constitutes, thanks to its key ability to produce relational goods, a driver of regional well-being.


INTRODUCTION
In recent decades, measuring and analysing the well-being of regions has gained considerable relevance in the field of regional sciences (Murias et al., 2012). Traditionally, the concept of well-being is intended in terms of material living conditions and measured, accordingly, through mainstream indicators such as gross domestic product (GDP) (Ayouba et al., 2020;Ferrara & Nisticò, 2019;Peiró-Palomino, 2019;Peiró-Palomino et al., 2020). However, following some important initiatives, such as the introduction of the human development index (United Nations Development Programme (UNDP), 1990) and the influential report by Stiglitz et al. (2009) on the measurement of economic performance and social progress, the use of GDP as an all-embracing indicator for assessing the quality of life began to be questioned since it is ineffective in measuring the degree to which society's goals are met (Calcagnini & Perugini, 2019a).
For the above reason, the most recent literature on well-being contains a variety of works that introduce composite indices or dashboards of indicators aimed at capturing the multidimensionality of the phenomenon by including, in addition to traditional macroeconomic indicators, measures related to spheres such as health, environment, education; that is, crucial factors in determining the quality of life of citizens .
The adoption of a multidimensional approach has led scholars and policymakers to assess more effectively the significant regional disparities that characterize many countries in terms of living standards, as reflected in income, health or education outcomes (Floerkemeier et al., 2021). Given that these disparities can undermine social cohesion, a better understanding of the drivers of multidimensional well-being could take on specific importance for policy design (Veneri & Murtin, 2019).
Recent studies (e.g., Calcagnini & Perugini, 2019b;Ferrara & Nisticò, 2019;Peiró-Palomino et al., 2020) have shown that certain socio-cultural and institutional factors, such as the quality of both formal and informal institutions, can positively impact multidimensional well-being. Following these works, we extend the investigation of those socio-cultural and institutional determinants of regional well-being, focusing on the potential virtuous role of the non-profit sector. With the term of non-profit, we intend that heterogeneous universe of organizations whose profits, unlike traditional firms, are fully reinvested in activities promoting the general interest, which is receiving particular attention in the economic literature due to its ascending economic importance and the role is acquiring in the territories meeting those social needs of citizens neglected by both the welfare state and the capitalist market economy (Cermelli et al., 2019a;García & Marcuello, 2002;Nissan et al., 2012).
As producers of social goods, non-profit organizations (NPOs) can be configured as a fundamental part of relational capital; that is, a majority (whether not coinciding) subset of social capital (Percoco, 2012a). Considering how social capital is widely recognized as a source of regional well-being (e.g., Botzen, 2016;Calcagnini & Perugini, 2019b;Terzo, 2021b), we hypothesize that the non-profit sector, since it assumes the feature of relational good (Percoco, 2012b), generate relational structures that can be exploited as productive resources helpful in sustaining economic prosperity and social and civic progress (Cermelli et al., 2019b;Terzo, 2021b). In order to test this hypothesis, which implies the presence of a positive relationship between the non-profit activity and regional well-being, we structure a cross-sectional analysis on a sample of 106 Italian provinces (NUTS-3) covering the period 2011-19, addressing both endogeneity and spatial dependence issues.
The choice of Italy as a case study has a twofold significance. This country, indeed, is distinguished by a nonprofit sector with an important tradition, which gave rise to crucial social innovationssuch as the development of the social cooperative modeland constitutes a pivot of the social economy, which plays a far from a marginal role within the Italian economic system (Terzo, 2021a). Moreover, due to its strong cultural heterogeneity, Italy constitutes a much-investigated case study in the field of social capital studies (e.g., Banfield, 1958;Crescenzi et al., 2013;Guiso et al., 2004;Nannicini et al., 2013;Putnam et al., 1994).
In the economic literature, there is not a great variety of empirical works that investigate the role of NPOs in fostering regional well-being and the quality of development in Italy. Scarlato (2012) highlights how social enterprises may have a pivotal role in Italian regions' welfare systems and development policies. Specifically, the author shows that social enterprises significantly contribute to regions' human development by carrying out activities that support people's capabilities. Through an exploratory analysis, Sabatini (2007) investigates the link between the territorial density of social cooperatives considered a proxy of bridging social capitaland the quality of development in Italian regions, showing a positive and statistically significant correlation. Percoco (2012a) empirically shows how non-profit firms, as an expression of relational social capital, support the economic development of Italian provinces. Terzo (2021a) investigates the role of social economy in the economic resilience processes of Italian provinces through the lens of social capital, showing how non-profit and cooperative organizations, when not driven by opportunistic and self-referential purposes, can help mitigate the impact of external shocks on the labour market. Terzo (2021b) empirically shows how social cooperatives can significantly contribute to increasing material living conditions in Italian provinces through the generation of social capital.
The present paper differs from the existing literature because, to the best of our knowledge, it should be the first work that empirically investigates the role of the Italian non-profit sectorconsidered in its totality and heterogeneity, and not referring exclusively to single legal forms that constitute itin fostering the multidimensional well-being at the local level. Thus, it is not limited to assessing single dimensions of well-being or the economic growth of Italian provinces, as done by previous studies on social economy and non-profit.
There is an essential aspect that, in our opinion, provides added value to this work. As argued by some authors (e.g., Calcagnini & Perugini, 2019b;Peiró-Palomino et al., 2020), while the literature on the measurement of multidimensional well-being, mainly aimed at assessing regional divides, is relatively well-established, the same cannot be argued concerning the spatial determinants of this phenomenon, since the existing studies focus mainly on single dimensions of well-being. Hence, we can contribute to the extension of a strand of literature that, to date, has not yet been fully explored in the field of regional sciences and that may be particularly fruitful for the policy implications it may have on the issue of socio-economic cohesion, which, as already pointed out, is of increasing importance for regional development policies, especially in the wake of the pandemic shock that has further exacerbated socio-spatial inequalities.
The remainder of the paper is structured as follows. In the following section we provide a theoretical framework regarding the link between the non-profit sector and regional well-being through a literature review. We then illustrate the methodologies related to measuring regional well-being and non-profit sector activity and continue describing the empirical strategy and showing the results of different econometric specifications. Finally, in the last section we develop some reflections on the findings of the empirical analysis and their possible implications for regional and local policies.

LINKS BETWEEN THE NON-PROFIT SECTOR AND REGIONAL WELL-BEING
The economic literature has several definitions of NPOs. Following Dobkin Hall (1987) (quoted in Bahmani et al., 2012), we consider an NPO as: a body of individuals who associate for any three purposes: (1) to perform public tasks that have been delegated to them by the state, (2) to perform public tasks for which there is a demand that neither the state nor for-profit organizations are willing to fulfil or (3) to influence the direction of policy in the state, the for-profit sector or other nonprofit organizations. (p.3) In essence, the non-profit sector represents a universe of institutions that, within the economic system, are placed between the state and the market, producing goods and services for civil society in its various expressions. The non-profit sector can contribute to regional wellbeing in several manners, not only by making an effective contribution to solving new social problems but also by strengthening its position as a necessary institution for stable and sustainable economic growth, fairer income and wealth distribution, matching services to needs, increasing the value of economic activities serving social needs, correcting labour market imbalances and, in short, deepening and strengthening economic democracy (Monzon & Chaves, 2008).
In this paper we focus on the relational dimension of the non-profit sector. As shown by several studies (e.g., Bauer et al., 2012;Birch & Whittam, 2008;Evans & Syrett, 2007), NPOs constitute both expression and source of social capital, which, referring to Putnam (1995), we conceive of as those 'features of a social organization such as norms, networks and trust that facilitate cooperation and coordination for mutual benefit' (p. 67). Specifically, NPOs can mainly encourage the creation of two forms of social capital: (1) bonding, which consists of strong ties between people belonging to the same social group, where substantial homogeneity, in terms of interests and values, is prevalent; and (2) bridging, consisting in the relationships between members of disparate groups, which facilitate the spread of generalized trust (Terzo, 2012a). Therefore, as Bassi (2013) argues, NPOs produce social added value by being featured by the presence of an internal relational dimension, which consists in the production of relational goodsthat is, interpersonal events that give relational outputs (Bruni et al., 2021) and an external relational dimension, which favours the accumulation of social capital through the performance of activities that promote social and civic progress. In addition to social added value, NPOs, again according to Bassi (2013), can also contribute to the generation of other forms of added value, including cultural added value, created through the dissemination of principles in the surrounding community that facilitate interpersonal relationssuch as fairness, tolerance, solidarity and mutuality.
The non-profit sector can significantly impact regional well-being by creating relational social capital. Specifically, the benefits from internal and external relational networks created by NPOs could be twofold.

MEASURING REGIONAL WELL-BEING AND NON-PROFIT SECTOR ACTIVITY
As we previously argued, to investigate the spatial distribution of well-being, a multidimensional approach is needed to grasp the complexity of a phenomenon that cannot be considered only in terms of material living conditions. Following the vast literature on the composite measurement of well-being, we individuate several variables collected from various databases, applying different rounds of data reduction based on statistical and economic criteria. 1 We finally consider 12 variables by means of a multicollinearity restriction exclusion, keeping only the variables correlated less than 80%. 2 The variables characterizing our multidimensional well-being index, which are listed in Table 1, can be broken down into eight domains: economic well-being; innovation; environment; labour market; education; participation; health; and safety. The elementary indicators represent the average of several years to cover as wide a period as possible, although, considering the limited availability of data at a NUTS-3 level, we also include single-year variables.
Regarding the weighting of these indicators, which is a much-debated issue in the literature, we adopt a system of 'equal weighting' (EW); that is, the most commonly used approach for weighting in multidimensional indices of well-being and the most appropriate solution when there is not enough information on subjective weightings of the variables used in the construction of the index (Decancq & Lugo, 2013;Hagerty & Land, 2007). The fundamental reason for this choice is that we consider, in line with the approach used by the Italian National Institute of Statistics (ISTAT) for the structuring of the Equitable and Sustainable Well-Being (BES) framework, all the indicators that make up our composite index of equal importance in determining the quality of life.
Concerning the normalization and aggregation of the elementary indicators, we adopt the adjusted Mazziotta-Pareto index (AMPI), a partially non-compensatory method also used by ISTAT for the construction of BES indices, whose robustness has been shown by different works (e.g., Mazziotta & Pareto, 2016. In this methodology, the aggregation is given by the arithmetic mean of the elementary indicators transformed by the min-max method and includes a penalty for horizontal variability. The AMPI has the advantage of penalizing geographical units with more unbalanced indicators, resulting in a non-constant replacement rate.
In this way, a variation in the value of one indicator cannot be perfectly compensated by the variation in another indicator, and the penalty will ensure that units with more balanced values of the elementary indicators are rewarded. Hence, the choice of this methodology is consistent with our view that the well-being domains should be as homogeneous as possible to ensure optimal living conditions. From a formal standpoint, the index is structured as follows. Given the matrix: where i ¼ 1, … , n are the units of analysis and j ¼ 1, … , m are the elementary indicators, we calculate the standardized matrix (r ij ) as follows: 60 + 70 If the indicator has a positive polarity 60 + 70 If the indicator has a negative polarity where x ij is the value of indicator j in unit i; and Min xj and Max xj are the two goalposts of indicator j. Denoting with M ri , S ri and CV i ¼ S ri /M ri the mean, standard deviation and coefficient of variation of the normalized values for unit i, respectively, the composite index is given by: In this case, subtracting from the mean the product between the standard deviation and coefficient of variation, we consider a composite index with a positive polarity, which can vary between 70 and 130. As previously argued, the index can be broken down into a 'mean effect' and a 'penalty effect'. The latter represents the penalty for horizontal variability, which, as already described, rewards units with less variability among elementary indicators by assigning them a higher value in the index. Figure 1 shows the geographical distribution of the index. As is widely expected, it reveals a significant difference in well-being levels between the Centre-North (where the highest values are concentrated) and the South, reflecting the traditional development divides characterizing Italy.
To measure the non-profit sector activity, we refer to the number of human resources of NPOs per 1000 inhabitants in 2011 (NPOs_HR). Specifically, it includes different categories of people who, in various capacities, operate in the multifaceted universe of the Italian non-profit sector; that is, the different categories of employees and volunteers. The choice of this indicator is based on the assumption that a greater presence in the territory of people working in NPOs corresponds to denser networks of relations and greater diffusion of valuessuch as reciprocity, solidarity and cooperationwhich favour the accumulation of social capital (Terzo, 2021b).
In the literature, there is extensive use of the number of NPOs to structure proxies for social capital. However, this indicator could be strongly biased by endogeneity since it does not discriminate between virtuous organizations that generate social value and those created for opportunistic and self-referential purposes. Using, as in our case, the number of human resources employed in NPOs allows endogeneity to be mitigated, considering that NPOs driven by particularistic interests are generally small in size, involving few people in their activities (Terzo, 2021a).
In Figure 2 we can observe the spatial distribution of the NPOs_HR indicator. It shows that the size of the non-profit sector, in terms of human resources employed, is more prominent in the Centre-North of the country, which is generally considered those with the highest social capital endowment.

ECONOMETRIC INVESTIGATION
As stated above, we hypothesize that the non-profit sector could be, thanks to its key ability to produce relational outputs, among those factors explaining the regional disparities of well-being characterizing Italy.
For this purpose, we develop an econometric model with cross-sectional data on 106 Italian provinces (NUTS-3). 3 The decision to use cross-sectional econometric modelling is constrained by the limited data available on NPOs. Hence, the standard solution of panel data estimation with fixed effects is not viable for our study.

Baseline model
We specify the following cross-sectional model for estimation: where subscript i refers to provinces; WB and NPOs_HR are the indicators of well-being and non-profit sector activity illustrated above; CONTROLS is a set of control variables useful to mitigate the omitted variable bias; θ indicates the macro-regional fixed-effects (North-West, North-East, Centre and South, with Islands as reference) included to control time-invariant area characteristics, and ε is an i.i.d. error term. Focusing on control variables, we include some indicators to proxy provinces' main economic, institutional and socio-cultural features that can impact regional well-being. The demographic structure, being able to determine the quantity and quality of human capital, can strongly influence regional well-being (Bloom et al., 2010;Lindh & Malmberg, 2009). For this motivation, we include a variable expressing the amount of resident population (POP) in our model, valid to control provinces' size. We also include a variable that indicates the average number of household components (HOUSEHOLD_SIZE)adopted, for instance, in Coccorese and Shaffer (2021) to proxy the strength of family ties, which can influence production, labour force participation of women and youngsters and geographical mobility (Alesina & Giuliano, 2010). Considering how the welfare state can have a positive impact on well-being by promoting human capabilities, we include in the model a variable indicating the per capita social services expenditure (SOC_EXP)employed, for   (2020), we control the sectoral composition of economic activity and regional specialization, including two variables that express the percentage of total value added represented by the manufacturing industries (MANUFACT) and the primary sector (PRI-MARY). All control variables, as well as the variable of interest, refer to 2011. This choice to lag the regressors is intended to mitigate the possible reverse causality bias. 4 Table 2 shows the baseline model results obtained by adopting an ordinary least squares (OLS) estimator with robust standard errors to rule out any bias coming from heteroscedasticity. In the first specification (column 1), we can see the estimation results by including only the variable of interest to check the unconditional correlation between WB and NPOs_HR. The second specification (column 2) includes the control variables, except for the macro-regional dummies, added only in the last specification (column 3). The results of these specifications show that our variable of interest has, in any case, positive and statistically significant coefficients at 1%, providing us with the first evidence of the role of NPOs as drivers of regional well-being.
Regarding the control variables, the positive sign of POP could indicate, for example, that a more populated area may increase the probability of matching job seekers and firms, which should improve the functioning of the labour market, positively impacting the overall wellbeing (Peiró-Palomino et al., 2020). The positive sign of HOUSEHOLD_SIZE can be interpreted considering that Italy is characterized by a Mediterranean welfare model where households play a pivotal role in coping with a limited offer of public services, acting as a social shock absorber (Alesina & Giuliano, 2011). The positive sign of SOC_EXP confirms that local social spending could positively impact well-being since fostering the provision of essential services promotes human development, affecting several domains of well-being such as health, education and material living conditions. The positive sign of MANUFACT could indicate that the most industrialized areas are traditionally those with the most significant economic prosperitywhich is generally associated with improvements in other dimensions of well-being, such as life expectancy and educational attainments (Organisation for Economic Co-operation and Development (OECD), 2013).
The Jarque-Bera tests and the average values of variance inflation factors (VIFs) show that our specifications are not biased by multicollinearity and non-normality of residuals issues. Furthermore, the F-tests reject in all cases the null hypothesis that the coefficients of our model are zero.

Extensions and robustness
We next explore several extensions of the baseline model to check the robustness of the previous evidence. First, we address the endogeneity bias. Regional wellbeing may be affected by the non-profit sector, but the latter may, in turn, be influenced by some of the well-being domains; hence, there could be a reverse causality issue, which the lagging of the explanatory variables can only mitigate. Furthermore, considering the limited number of control variables included in the model, due to the paucity of NUTS-3 data, we cannot rule out the possible presence of omitted variable bias. To tackle these issues, we follow the mainstream method to deal with endogeneity: the instrumental variables (IV) approach, using a twostage least squares (2SLS) estimator.
Regarding the choice of instruments, the criterion we adopt for their selection is to isolate the impact of those virtuous organizations that generate social value, which can be essential to stimulate regional well-being. In particular, we refer to two different variables. The first instrument indicates the number of market-oriented NPOs per 1000 inhabitants in 2011 (NPOs_market). This variable can be a good candidate as an instrument because market-oriented NPOs could be, thanks to their greater financial autonomy, minor subject to external pressure that could distract them from pursuing social goals (Poledrini, 2015). The second instrument is the percentage of NPOs active in 2011 established before 1970 (NPOs_hist). The rationale for including this variable as an instrument is that the significant presence of historical NPOs can indicate a strong persistence of individuals' behaviours and social values. Therefore, we assume that it is positively correlated with the NPOs_HR variable because of the path dependence characterizing the social behaviour of individuals (Percoco, 2012a). Table 3 shows the results of both the first and second stages of the IV-2SLS estimation. First, we can observe that the F-statistics of the first stage is 77.06; therefore, we conclude that the instruments are not weak. In column (1), which illustrates the results of the first stage estimation, we can see as both instrumental variables have positive and statistically significant coefficients. Moreover, the over-identification test indicates that the instruments are exogenous and thus uncorrelated with the error term. This estimation confirms the positive association between NPOs_HR and WB, which is, therefore, robust to endogeneity.
We also estimate the baseline model using alternative methods to structure our dependent variable. First, we employ a generalized mean aggregation method that, following Pinar (2019), can be formalized as: Non-profit sector and regional well-being in Italy 469 where w j is the weight attached to indicator j; and r ij is the normalized achievement level of a province i in indicator j. The parameter β captures the degree of substitution (complementarity) among the indicators. Following the strategy of the author previously cited (Pinar, 2019), we structure two different indices according to the value assigned to β. First, we consider β ¼ 1 (WB_mean), which leads to the computation of arithmetic mean, implying perfect substitutability among indicators. Second, we consider β ¼ 0 (WB_geomean), by which the aggregation function becomes a geometric mean, reflecting some degree of complementarity among indicators rather than perfect substitutability. In these two cases, we assign to all indicators the same weight. Following Ciommi et al. (2017), we introduce two other indices. The first is a weighted average of the elementary indicators with a weight given by the Gini index of each indicator, normalized by the sum of the Gini indices of all indicators (WB_GW). We can formalize this method as follows: where G. j indicates the Gini coefficient of indicator j; and G the sum of G. j . The weights, therefore, depend on a coefficient of vertical variability; a more homogeneous distribution of the j-th indicator implies a higher weighting. The second index is a variant of the AMPI methodology called the Gini-adjusted Mazziotta Pareto index (GAMPI). Specifically, we modify the AMPI by computing first a Gini-based weighted average of the elementary indicators (GW), then adjusted by the penalty function. Hence, we can rewrite equation (3) as follows: Table 4 shows the OLS estimates results using, as dependent variables, the well-being indices computed with the methods above explained. Our variable of interest coefficients remains positive and statistically significant in all cases. Overall, we can state that the results obtained using alternative weighting methods and aggregation validate our composite index's robustness.
We further estimate the baseline model using different dependent variables representing the single domains of our Note: All estimates include a constant term (not shown). All variables included in the model are log-transformed. Robust standard errors are shown in parentheses. ***p < 1%; **p < 5%; *p < 10%. VIF, variance inflation factor.
well-being index; that is, economic well-being, innovation, environment, labour market, health, education, safety and participation. 5 As we can observe in Table 5, the different specifications highlight how the non-profit sector significantly impacts on all domains chosen to structure the composite index of well-being. We now test the robustness of the previous evidence using alternative indicators on the non-profit sector activity. First, we have to consider that the non-profit sector consists of various organizations with different structures and aims. In order to consider this heterogeneity, we include in the baseline model, in substitution of the variable NPOs_HR, some indicators expressing the number of human resources per 1000 inhabitants in 2011 of the following organizations: (1) social cooperatives (SOC_-COOP); (2) associations (ASSOC); (3) foundations (FOUND); and (4) other organizations (OTHER_NPOs). 6 Table 6 shows that all variables previously listed have coefficients with positive and statistically significant signs, except for the variable OTHER_NPOs.
Finally, we split the NPOs_HR variable into two variables: the number of employees (NPOs_emp) and the number of volunteers (NPOs_volunt) per 1000 inhabitants. The results of different specifications, shown in Table 7, further confirm the non-profit sector's role as a driver of regional well-being.
All model specifications shown in this subsection show no concerns with multicollinearity and non-normality of the residuals and their predictive capacity. The models show consistent results with those observed in the baseline model regarding the control variables. The only exception is model 4, where the variable HOUSEHOLD_SIZE takes on different signs depending on the dependent variable adopted. The negative relationship that this variable has with the indicators of economic well-being, innovation and education is consistent with the reasoning of Banfield (1958), Coleman (1988, 1990 and Granovetter (1973), who claims that in a society where people are raised to trust only their family networks, they are also taught to distrust people outside the family; this carries the risk of limiting the circulation of new ideas and innovation and the accumulation of human capital, which can negatively affect economic prosperity (Sabatini, 2009). The other results can be interpreted considering, as previously claimed, that households, acting as social shock absorbers, can contribute to the safety and health of regions. However, Alesina and Giuliano (2011) observed that the more individuals rely on the family as providers of services, insurance, and transfer of resources, the lower one's civic engagement and political participation.

Spatial analysis
It is important to note that Figure 1 suggests that the level of well-being is not randomly distributed across space in Italy. On the contrary, there seem to be spatial clusters of provinces with similar levels of well-being, while there are few cases in which a province shows a markedly different performance from its neighbours. This reasoning is consistent with the evidence provided by Figure 3, which shows the scatterplot of the global Moran index and the cluster and significance maps of the local Moran index, created using a distance-based matrix (cut-off threshold ¼ 120 km). 7 They reveal a positive and robust link between own well-being and the average of neighbouring provinces, indicating that the regional distribution of high and/or low values of the measure of well-being is more spatially clustered than would be expected if the underlying spatial processes were random.
Considering that the implications of spatial dependence are potentially crucial from an econometric perspective (Anselin, 1988), we also decide to carry out spatial econometric analysis. In order to choose the most appropriate spatial model to estimate, we test our baseline model for the presence of two possible forms of autocorrelation: the Lagrange multiplier (LM) tests for an omitted spatial lag (LMlag) and an omitted spatial error (LMerr).  Table 8, which shows the diagnostic tests for spatial dependence, estimated through adopting a matrix obtained from a 120 km threshold, suggests a spatial autoregressive model (SAR) as the most appropriate choice.
We thus consider the following spatial cross-sectional model: Compared with equation (4), here we add a spatially lagged dependent variable (ρW*WB) as an additional control, where ρ is the spatial autoregressive coefficient, which tests whether the level of well-being may spillover from nearby provinces (LeSage & Pace, 2009); and W is a spatially weighted matrix.
The SAR model is generally estimated through a maximum likelihood (ML) estimator. However, to check for the robustness of our results, we consider an additional estimation technique, namely the spatial two-stage least squares (S2SLS) (Kelejian & Prucha, 1998). In this case, the spatial autoregressive term is instrumented through internal instruments consisting of the first and second spatial lags of the independent variables (WX, W 2 X ).
We first estimate these models using a distance-based matrix (cut-off threshold ¼ 120 km). Then, to check whether the results are not sensitive to the choice of the weighting matrix, we also estimate them using a k-nearest neighbours (KNN) matrix with 10 as the critical cut-off for each province. 8 We also select this matrix typology because it allows us to choose a fixed number of neighbours; this is relevant in our work because we deal with highly irregular geographical areas such as Italian provinces. According to Le Gallo and Ertur (2003), selecting a fixed number of neighbours avoids potential methodological concerns when estimating complex regression models.
These estimations confirm the positive and statistically significant relationship between NPOs_HR and WB. Furthermore, the control variables keep the same signs observed in the baseline model. As we can see at the bottom of Table 9, the Anselin-Kelejian test (Anselin & Kelejian, 1997) indicates no remaining spatial autocorrelation in the residuals; we thus effectively address the spatial dependence issue.

CONCLUSIONS
We investigated the non-profit sector's role in fostering regional well-being through this paper, focusing on its main feature as a social and relational capital source. We hypothesized that when there is more non-profit in a province, people will build more considerable relational capital, which, by facilitating communication and coordination, creates an atmosphere of trust that could significantly enhance the regional well-being. We searched for validation of our hypothesis conducting a cross-sectional analysis on a sample of 106 Italian provinces. Our findings, robust to several issues and scenarios, confirm that the non-profit sector can be among those factors explaining regional disparities of wellbeing that characterize Italy. Such evidence appears particularly promising and could help direct future research towards a better understanding of the relevance of the non-profit sector in the regional and local economic system. In our opinion, the most important aspect is to show how the non-profit sectorconsidered not as a mere sector that plays a residual role within the economic system, filling the gaps in the welfare state and the capitalist market economyis not only the product of the social capital of a territory, which indirectly promotes regional wellbeing but also, and above all, a key player which, by combining the generation of economic and social value, can take on crucial importance in promoting a development model that is more oriented towards people's real needs, significantly improving their quality of life. This argument has, clearly, important policy implications since, in the light of this, we believe that the non-profit sector may play a leading role in the context of a new vision of welfare which, by supplanting the traditional welfare state model that has revealed all its limitations with the recent crises, is based on generativity, which implies that the whole society, and not only the state, must take responsibility for sustaining the well-being of the community (Bruni & Zamagni, 2007). This is what we can call 'civil welfare', within which organized civil society can play a vital role as the glue between the various spheres of society, which must take charge of the design and implementation of welfare policies at the local level. In order to promote the transition process towards civil welfare, it is necessary to recognize, both at a political and regulatory level, the central role that the non-profit sector is assuming in the economic system, which renders obsolete its label of 'third sector'i.e., as previously stated, a sector that carries out an activity aimed at correcting the failures of the state and the market. In line with the provisions of the 'Reform of the Third Sector' launched in Italy in 2016 and still in the process of being completed, the aim of policy-makers should be to encourage the autonomous initiative of citizens in carrying out activities of general interest, implementing a principle of circular subsidiarity that equally articulates the relations between the state, the market and the community in a perspective of mutual cooperation.

DISCLOSURE STATEMENT
No potential conflict of interest was reported by the authors.

NOTES
1. Specifically, we use the ISTAT databases 'I.Stat', 'BES of the territories' and 'Territorial indicators for development policies', as well as the territorial statistics of the Centro Studi G. Tagliacarne. 2. The only exception is the correlation between the unemployment rate and average disposable income per capita, which is -0.82. In this case, we keep both variables as their joint use is quite common in structuring composite indices of well-being (e.g., Peiró-Palomino et al., 2019. For the correlation matrix of the variable constituting the composite index, see Table A1 in the supplemental data online. 3. We do not consider the province of South Sardinia because of lack of data. 4. The summary statistics of the variables included in the econometric analysis and the correlation matrix of the covariates are shown in Tables A2 and A3, respectively, in the supplemental data online. 5. The domains with multiple variables result from the aggregation of elementary indicators using the AMPI methodology, attributing a positive polarity. 6. The variable includes human resources from ecclesiastical bodies, committees, mutual aid societies, health and educational institutions, and social enterprises. For a brief description of the different organizations constituting the Italian non-profit sector, see Table A4 in the supplemental data online. 7. Due to the removal of the province of South Sardinia for lack of data, we would have isolated provinces using a traditional contiguity matrix. For this reason, we use a matrix based on 120 km centroid distances so that each province has at least one neighbour. We standardize this matrix using the row standardization method. 8. We choose a KNN 10 matrix because it guarantees the best model fit, unlike the others.